A topological characterisation of holomorphic parabolic germs in the plane
Dynamical Systems
2007-09-11 v1
Abstract
Gambaudo and P\'ecou introduced the ``linking property'' to study the dynamics of germs of planar homeomorphims and provide a new proof of Naishul theorem in their paper "A topological invariant for volume preserving diffeomorphisms" (Ergodic Theory Dynam. Systems 15 (1995), no. 3, 535--541). In this paper we prove that the negation of Gambaudo-P\'ecou property characterises the topological dynamics of holomorphic parabolic germs. As a consequence, a rotation set for germs of surface homeomorphisms around a fixed point can be defined, and it will turn out to be non trivial except for countably many conjugacy classes.
Keywords
Cite
@article{arxiv.0709.1398,
title = {A topological characterisation of holomorphic parabolic germs in the plane},
author = {Frédéric Le Roux},
journal= {arXiv preprint arXiv:0709.1398},
year = {2007}
}